# ---
# title: 1519. Number of Nodes in the Sub-Tree With the Same Label
# id: problem1519
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Depth-first Search, Breadth-first Search
# link: <https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/description/>
# hidden: true
# ---
# 
# Given a tree (i.e. a connected, undirected graph that has no cycles)
# consisting of `n` nodes numbered from `0` to `n - 1` and exactly `n - 1`
# `edges`. The **root** of the tree is the node `0`, and each node of the tree
# has **a label** which is a lower-case character given in the string `labels`
# (i.e. The node with the number `i` has the label `labels[i]`).
# 
# The `edges` array is given on the form `edges[i] = [ai, bi]`, which means
# there is an edge between nodes `ai` and `bi` in the tree.
# 
# Return _an array of size`n`_ where `ans[i]` is the number of nodes in the
# subtree of the `ith` node which have the same label as node `i`.
# 
# A subtree of a tree `T` is the tree consisting of a node in `T` and all of its
# descendant nodes.
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2020/07/01/q3e1.jpg)
# 
#     
#     
#     Input: n = 7, edges = [[0,1],[0,2],[1,4],[1,5],[2,3],[2,6]], labels = "abaedcd"
#     Output: [2,1,1,1,1,1,1]
#     Explanation: Node 0 has label 'a' and its sub-tree has node 2 with label 'a' as well, thus the answer is 2. Notice that any node is part of its sub-tree.
#     Node 1 has a label 'b'. The sub-tree of node 1 contains nodes 1,4 and 5, as nodes 4 and 5 have different labels than node 1, the answer is just 1 (the node itself).
#     
# 
# **Example 2:**
# 
# ![](https://assets.leetcode.com/uploads/2020/07/01/q3e2.jpg)
# 
#     
#     
#     Input: n = 4, edges = [[0,1],[1,2],[0,3]], labels = "bbbb"
#     Output: [4,2,1,1]
#     Explanation: The sub-tree of node 2 contains only node 2, so the answer is 1.
#     The sub-tree of node 3 contains only node 3, so the answer is 1.
#     The sub-tree of node 1 contains nodes 1 and 2, both have label 'b', thus the answer is 2.
#     The sub-tree of node 0 contains nodes 0, 1, 2 and 3, all with label 'b', thus the answer is 4.
#     
# 
# **Example 3:**
# 
# ![](https://assets.leetcode.com/uploads/2020/07/01/q3e3.jpg)
# 
#     
#     
#     Input: n = 5, edges = [[0,1],[0,2],[1,3],[0,4]], labels = "aabab"
#     Output: [3,2,1,1,1]
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: n = 6, edges = [[0,1],[0,2],[1,3],[3,4],[4,5]], labels = "cbabaa"
#     Output: [1,2,1,1,2,1]
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: n = 7, edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]], labels = "aaabaaa"
#     Output: [6,5,4,1,3,2,1]
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 10^5`
#   * `edges.length == n - 1`
#   * `edges[i].length == 2`
#   * `0 <= ai, bi < n`
#   * `ai != bi`
#   * `labels.length == n`
#   * `labels` is consisting of only of lower-case English letters.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
